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SUMMARY:The work of Matomaki and Radziwill on average value of the \\lambd
 a function
DTSTART:20151001T141500
DTEND:20151001T151500
DTSTAMP:20260428T051501Z
UID:d8c6a9e1ec1dc671a7a3efd124e4004625cde9634ca9196b4eef48be
CATEGORIES:Conferences - Seminars
DESCRIPTION:Harald Helfgott - Georg-August-Universität Göttingen\nLet f 
 be a multiplicative function. Let $h = h(x)\\to infty$ (arbitrarily slowly
 ) when $x\\to \\infty$. Kaisa Matomaki and Maksym Radziwill have proved th
 at\, for a proportion tending to 1 of all X\\leq x\\leq 2X\, the average o
 f f(n) from x to x+h is within o(1) of the average of f(n) from x to 2x.\n
 This result - whose proof is remarkably elegant and straightforward - is m
 uch stronger than what was known before\, even for specific multiplicative
  functions. For example\, for f = mu or f = lambda (the Moebius and Louivi
 lle functions)\, we had such results only for h>=x^(1/6).\nThere have alre
 ady been applications towards Chowla's conjecture (in part by Matomaki-Rad
 ziwill and in part by Tao\, or both). We will go over the proof for f = la
 mbda.\nThe talk is meant to be an incentive to a discussion in depth of th
 ese recent results.
LOCATION:CM 1 121 http://plan.epfl.ch/?room=CM%201%20121
STATUS:CONFIRMED
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